This dissertation is an effort to adapt two classical non-parametric statistical techniques, kernel density estimation (KDE) and principal components analysis (PCA), to the Billera-Holmes-Vogtmann (BHV) metric space for phylogenetic trees. This adaption gives a more general framework for developing and testing various hypotheses about apparent differences or similarities between sets of phylogenetic trees than currently exists. For example, while the majority of gene histories found in a clade of organisms are expected to be generated by a common evolutionary process, numerous other coexisting processes (e.g. horizontal gene transfers, gene duplication and subsequent neofunctionalization) will cause some genes to exhibit a history quite distinct from the histories of the majority of genes. Such “outlying” gene trees are considered to be biologically interesting and identifying these genes has become an important problem in phylogenetics. The R sofware package kdetrees, developed in Chapter 2, contains an implementation of the kernel density estimation method. The primary theoretical difficulty involved in this adaptation concerns the normalizion of the kernel functions in the BHV metric space. This problem is addressed in Chapter 3. In both chapters, the software package is applied to both simulated and empirical datasets to demonstrate the properties of the method. A few first theoretical steps in adaption of principal components analysis to the BHV space are presented in Chapter 4. It becomes necessary to generalize the notion of a set of perpendicular vectors in Euclidean space to the BHV metric space, but there some ambiguity about how to best proceed. We show that convex hulls are one reasonable approach to the problem. The Nye-PCA- algorithm provides a method of projecting onto arbitrary convex hulls in BHV space, providing the core of a modified PCA-type method.

Fusarium head blight (FHB), caused by Fusarium graminearum Schwabe [telomorph: Gibberella zeae Schwein.(Petch)], is recognized as one of the most destructive diseases of wheat (Triticum aestivum L. and T. durum L.) and barley (Hordeum vulgare L.) worldwide. Breeding for FHB resistance must be accompanied by selection for desirable agronomic traits. Donor parents with two FHB resistance quantitative trait loci (QTL) Fhb1 (chromosome 3BS) and QFhs.nau-2DL (chromosome 2DL) were crossed to four adapted SRW wheat lines to generate backcross and forward cross progeny. F2 individuals were genotyped and assigned to 4 different groups according to presence/ absence of one or both QTL. The effectiveness of these QTL in reducing FHB in F2 derived lines was assessed in a misted, inoculated scab nursery. Resistance alleles and the interaction among FHB resistance QTL have distinct behavior in different genetic backgrounds in wheat. Fhb1 showed an average disease reduction of 12%, however it did not result in significant improvement of FHB resistance in all populations. In general, for the four backgrounds studied, the QFhs.nau-2DL QTL as more effective reducing FHB (19% average reduction). The combination of Fhb1 and QFhs.nau-2DL is not necessary, but recommended and it improved resistance in all populations. Backcross derived (BC) progeny from four genetic backgrounds were planted in replicated plots (2011 and 2012) and in the scab nursery in 2012. Population 2 had its progeny characterized by 961 DArT markers distributed throughout the genome. Several high-quality polymorphic markers were identified and listed as good predictors of phenotypic traits like disease resistance, and improved agronomic and quality characteristics. Backcross and forward cross derived progenies were tested for FHB resistance and agronomic and baking quality performance for 4 different populations sharing the same donor parent for resistance QTL. The results confirmed that F2 populations were effective indicators of expression levels of QTL prior to extensive backcrossing. The QTL Fhb1 and QFhs.nau-2DL increased FHB resistance without detriments on agronomic and quality traits on wheat populations investigated. BC populations were assessed as breeding populations and established as being rewarding tools for derivation of inbred lines in a breeding program, being BC2 the most recommended from our results.

i Abstract The purpose of this project is to compare two statistical approaches, traditional multivariate analysis and Bayesian networks, for representing the relationship between volatile compounds in kiwifruit. Compound measurements were for individual vines which were progeny of an intercross. It was expected that groupings in the data (or compounds) would give some indication of the generic nature of the biochemical pathways. Data for this project was provided by the Flavour Biotech team at Plant and Food Research. This data contained many non-detected observations which were treated as zero and to deal with them, we looked for appropriate value of c for data transformation in log(x+c). The data is ‘large p small n’ paradigm – and has much in common with data, although it is not as extreme as microarray. Principal component analysis was done to select a subset of compounds that retained most of the multivariate structure for further analysis. The reduced set of data was analyzed by Cluster analysis and Bayesian network techniques. A heat map produced by Cluster analysis and a graphical representation of Bayesian networks were presented to scientists for their comments. According to them, the two graphs complemented each other; both graphs were useful in their own unique way. Along with clusters of compounds, clusters of genotypes were represented by the heat map which showed by how much a particular compound is present in each genotype while the relation among different compounds was seen from the Bayesian networks.

This thesis presents models that describe the behaviour of electricity demand and ambient temperature. Important features of both variables are described by mathematical components. These models were developed to calculate the value of electricity demand that is not expected to be exceeded more than once in ten years and to generate synthetic sequences that can be used as input data in simulation software. / PhD Doctorate

Submitted by (ana.araujo@ufrpe.br) on 2016-05-18T17:21:28Z No. of bitstreams: 1 Adriano Victor Lopes da Silva.pdf: 1127667 bytes, checksum: aa52cc1c83e4335d093e8d62132c37bd (MD5) / Made available in DSpace on 2016-05-18T17:21:28Z (GMT). No. of bitstreams: 1 Adriano Victor Lopes da Silva.pdf: 1127667 bytes, checksum: aa52cc1c83e4335d093e8d62132c37bd (MD5) Previous issue date: 2008-02-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The objective of this work was to use univariate and multivariate statistical methods on selection of independent variables, in the mathematical linear models, to estimate the green biomass of the main bamboo rod, bambusa vulgaris, pursuing time and cost reduction without loss of precision. The data came from an experiment carried out for the Agroindustrial Excelsior S. A. (Agrimex) company located in the city of Goiana – PE.Quantified by its green biomass weight,450 bamboo rods were used and 4 independent variables measured in the rod. Initially, the effect of the multicollinearity could be verified through the correlation matrix of the independent variables and the varience inflation factors.To select the independent variables two methods were used: Stepwise and K component retention. The alternatives used were component regression and Ridge regression. In general, in only one situation the variable selection methods behave adequately while multicollinearity is present among the independent variables, that is the multivaried method of retention K=3 component for the covariate matrix, model of Spurr. The estimative of alternative methods showed similar responses, however, the principal component regression yields the best results. / O objetivo deste trabalho foi utilizar métodos estatísticos univariado e multivariado na seleção de variáveis independentes, em modelos matemáticos lineares para a estimativa da biomassa verde da haste principal do bambu, Bambusa vulgaris, visando reduzir tempo e custo sem perda de precisão, além de empregar alternativas para estimação na existência de multicolinearidade. Os dados foram provenientes de um experimento conduzido pela empresa Agroindustrial Excelsior S. A. (Agrimex) localizada no Engenho Itapirema na cidade de Goiana – PE. Foram utilizadas 450 hastes de bambu, que tiveram sua biomassa verde quantificada através do peso e 4 variáveis independentes medidas na mesma haste. Inicialmente, verificou-se a existência da multicolinearidade por meio da matriz de correlação das variáveis independentes e pelo fator de inflação da variância. Para seleção das variáveis independentes foram utilizados os métodos:Stepwise e Retenção por K componentes. As alternativas utilizadas foram a Regressão com os componentes principais e Regressão Ridge. No geral, em apenas uma situação os métodos de seleção de variáveis se comportam adequadamente na existência de multicolinearidade entre as variáveis explicativas, exatamente o método multivariado de retenção por K=3 componente pela matriz de covariância, modelo de Spurr. Os métodos alternativos de estimação conduzem respostas semelhantes, mesmo que possuindo estruturas diferentes, no entanto, a regressão com os componentes principais obteve os melhores resultados.

Enquanto a Administração de Empresas evoluiu muito no último século e trouxe vasto ferramental aos gestores de empresas, o tema da Responsabilidade Social Empresarial (RSE) não acompanhou essa evolução e ainda não dispõe de conceitos sólidos e ferramental de apoio aos gestores. Isso justifica o presente estudo, que objetiva identificar, empiricamente, o comportamento das empresas que operam no Brasil, referente aos seus investimentos em ações de RSE e suas relações com o Desempenho Financeiro (DF), com base na Receita Líquida (RL) e no Resultado Operacional (RO). A partir de uma amostra de 2064 Balanços Sociais padrão IBASE (BS) de 378 empresas, no período entre 1996 e 2010, o estudo buscou resposta a oito perguntas de pesquisa e encontrou comportamentos estatisticamente significativos em todas elas. Os resultados indicam que existe relacionamento direto entre a RL e os investimentos em RSE. Existe também um relacionamento direto entre o RO-Positivo e os investimentos em RSE. Nos casos em que o RO é negativo, o relacionamento com os investimentos em RSE está associado ao valor absoluto do RO-Negativo, o que pode ser uma relação dependente da RL ou do porte da empresa. O setor de atuação das empresas é um fator que segmenta comportamentos característicos das empresas e nem todas as turbulências conjunturais nacionais e internacionais impactam e influenciam as decisões de investimentos em RSE e o DF das empresas de forma semelhante. Os modelos matemáticos que relacionam a RL com os investimentos em RSE têm melhor capacidade explicativa que os modelos correspondentes que relacionam o RO a esses mesmos investimentos, sendo que o setor de atuação é um diferenciador significativo. Não foram encontradas diferenças significativas na qualidade explicativa dos modelos matemáticos que consideraram o DF do ano-base e do ano anterior em relação às decisões de investimentos em RSE e, mais, a composição do portfólio de investimento em RSE varia em função do setor e do ano de publicação dos BSs. / While Business Management was much developed during the last hundred years and accumulated a lot of management tools to managers of companies, the theme of Corporate Social Responsibility (CSR) has only received tangential attention and does not yet have solid concepts and tools to support managers. This lack of similar evolution justifies the present study, which aims to identify, empirically, the behavior of companies operating in Brazil, related to their investments in activities of CSR and its relations with Financial Performance (FP), based on Net Income (NI) and Operational Results (OR). From a sample of 2064 IBASE Social Accounting Balances (SAB) of 378 companies between 1996 and 2010, the study sought to answer eight research questions and found statistically significant behavior in all of them. The results indicate that there is direct relationship between the NI and investments in CSR. There is also a direct relationship between the ORPositive and investments in CSR. When OR is negative, the relationship between CSR investment is associated with the absolute value of OR-negative, which may be a dependent relationship of NI or size of the company. The business sector is a factor that segments the characteristic behaviors of companies, and not all national and international economic turmoil impact and influence investment decisions in CSR and FP of firms with the same magnitude. The mathematical models that relate the NI with investments in CSR have better explanatory power than models that relate the OR corresponding to such investments, and the sector of activity is a significant differentiator. There were no significant differences in the explanatory quality of mathematical models that considered the FP for the base year and the year before, in relation to decisions on investments in CSR,, and the composition of the investment in CSR portfolio varies by sector and year of publication of SABs.

We introduce a new class of measures for testing independence between two random vectors, which uses expected difference of conditional and marginal characteristic functions. By choosing a particular weight function in the class, we propose a new index for measuring independence and study its property. Two empirical versions are developed, their properties, asymptotics, connection with existing measures and applications are discussed. Implementation and Monte Carlo results are also presented. We propose a two-stage sufficient variable selections method based on the new index to deal with large p small n data. The method does not require model specification and especially focuses on categorical response. Our approach always improves other typical screening approaches which only use marginal relation. Numerical studies are provided to demonstrate the advantages of the method. We introduce a novel approach to sufficient dimension reduction problems using the new measure. The proposed method requires very mild conditions on the predictors, estimates the central subspace effectively and is especially useful when response is categorical. It keeps the model-free advantage without estimating link function. Under regularity conditions, root-n consistency and asymptotic normality are established. The proposed method is very competitive and robust comparing to existing dimension reduction methods through simulations results.

Goodness-of-fit tests have been studied by many researchers. Among them, an alternative statistical test for uniformity was proposed by Chen and Ye (2009). The test was used by Xiong (2010) to test normality for the case that both location parameter and scale parameter of the normal distribution are known. The purpose of the present thesis is to extend the result to the case that the parameters are unknown. A table for the critical values of the test statistic is obtained using Monte Carlo simulation. The performance of the proposed test is compared with the Shapiro-Wilk test and the Kolmogorov-Smirnov test. Monte-Carlo simulation results show that proposed test performs better than the Kolmogorov-Smirnov test in many cases. The Shapiro Wilk test is still the most powerful test although in some cases the test proposed in the present research performs better.

<div>Physical phenomena in nature are typically represented by complex systems of ordinary differential equations (ODEs) or partial differential equations (PDEs), modeling a wide range of spatio-temporal scales and multi-physics. The field of computational science has achieved indisputable success in advancing our understanding of the natural world - made possible through a combination of increasingly sophisticated mathematical models, numerical techniques and hardware resources. Furthermore, there has been a recent revolution in the data-driven sciences - spurred on by advances in the deep learning/stochastic optimization communities and the democratization of machine learning (ML) software.</div><div><br></div><div><div>With the ubiquity of use of computational models for analysis and prediction of physical systems, there has arisen a need for rigorously characterizing the effects of unknown variables in a system. Unfortunately, Uncertainty quantification (UQ) tasks such as model calibration, uncertainty propagation, and optimization under uncertainty, typically require several thousand evaluations of the underlying physical models. In order to deal with the high cost of the forward model, one typically resorts to the surrogate idea - replacing the true response surface with an approximation that is both accurate as well cheap (computationally speaking). However, state-ofart numerical systems are often characterized by a very large number of stochastic parameters - of the order of hundreds or thousands. The high cost of individual evaluations of the forward model, coupled with the limited real world computational budget one is constrained to work with, means that one is faced with the task of constructing a surrogate model for a system with high input dimensionality and small dataset sizes. In other words, one faces the <i>curse of dimensionality</i>.</div></div><div><br></div><div><div>In this dissertation, we propose multiple ways of overcoming the<i> curse of dimensionality</i> when constructing surrogate models for high-dimensional numerical simulators. The core idea binding all of our proposed approach is simple - we try to discover special structure in the stochastic parameter which captures most of the variance of the output quantity of interest. Our strategies first identify such a low-rank structure, project the high-dimensional input onto it, and then link the projection to the output. If the dimensionality of the low dimensional structure is small enough, learning the map between this reduced input space to the output is a much easier task in</div><div>comparison to the original surrogate modeling task.</div></div>

Many tools exist to assist law enforcement agencies in mitigating criminal activity. For centuries, academics used statistics in the study of crime and criminals, and more recently, police departments make use of spatial statistics and geographic information systems in that pursuit. Clustering and hot spot methods of analysis are popular in this application for their relative simplicity of interpretation and ease of process. With recent advancements in geospatial technology, it is easier than ever to publicly share data through visual communication tools like web applications and dashboards. Sharing data and results of analyses boosts transparency and the public image of police agencies, an image important to maintaining public trust in law enforcement and active participation in community safety.